Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 8$ and $ JT = 5x - 5$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 8} = {5x - 5}$ Solve for $x$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({3}) - 8$ $ JT = 5({3}) - 5$ $ CJ = 18 - 8$ $ JT = 15 - 5$ $ CJ = 10$ $ JT = 10$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {10} + {10}$ $ CT = 20$